Gradient descent iterative method for energy flow of integrated energy system considering multiple modes of compressors

Energy flow plays an important role in optimal operation and planning analysis of integrated energy systems. However, in the energy flow calculation of integrated energy systems, the model of natural gas networks is inaccuracy. In traditional models, the gas compressor is modeled with a single compression ratio, without regard for the impact of different operating modes on energy flow. However, compressors often operate in different modes, so the constant compression ratio model will lead to inaccurate results of energy flow. To enhance the accuracy of energy flow, multiple compressor operating modes are considered in this paper, including constant compression ratio mode, constant outlet pressure mode, and constant natural gas flow mode. Also, for conciseness, the three modes are unified formulated by a general equation. Then, to ascertain the energy flow, a complete gradient descent iterative method is proposed, in which the partial derivatives of each state variable are calculated, and a new Jacobian matrix is derived. Compared with the non-gradient descent method, the computational speed of the proposed method is faster while the computational accuracy has not been reduced. The results tested on 14 node electricity-14 node heat-10 node gas and 1047 node electricity-32 node heat-48 node gas integrated systems show that the operating modes of compressors have great influences on the gas pressure distribution, which further affect the distributions of electricity and heat. Also, the superiority of the proposed gradient descent method is verified.